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中文摘要：
提出了一种适用于裂尖改进单元的新型改进函数，基于三角变换的方法，保留裂纹尖端场的应力奇异性和裂纹上、下表面的位移不连续性，将常规扩展有限元法裂尖改进单元的4项改进函数缩减为2项，裂尖改进单元的结点由常规的8个改进自由度减少为4个．采用2个正交的水平集函数表征材料内部裂纹面，详细阐述了改进单元类型的判别方法，给出一种改进单元的分区域积分方案．最后，若干断裂力学问题经典算例的数值计算结果表明：建议的裂尖改进函数具有较高的数值精度，该方法是十分有效的．
英文摘要：
In the paper, a novel enriched function for those elements containing crack tip is proposed. By the method of trigonometric transform, the four crack tip enriched functions in the standard extended finite element methods （XFEM） are reduced to the two ones. The reduced enriched functions still keep the two properties, such as the stress singular at the crack tip and the discontinuities of crack surfaces. The enriched degrees of freedom for those nodes of element containing crack tip is thereby reduced from 8 to 4. The two orthogonal level set functions are used to represent the existing crack in materials. The method for identifying the enriched type of elements is described in details. An integration schemes for enriched elements are given. Finally, several classic fracture problems are given to verify the numerical precision of the proposed crack tip enriched functions. The results show the effectiveness of the proposed method.
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